| Linear | Semilog | Growth | Spline without knots | Spline with knots | ARIMA | |
|---|---|---|---|---|---|---|
| (Intercept) | 309.718 **** | -61.807 | 4.679 **** | -4.427 | 79.837 | |
| (34.859) | (93.889) | (0.140) | (62.400) | (153.383) | ||
| Day | 0.105 | 0.001 *** | ||||
| (0.116) | (0.000) | |||||
| log(Day) | 75.814 **** | |||||
| (17.539) | ||||||
| bs(Day, knots = NULL)1 | 518.671 *** | |||||
| (180.305) | ||||||
| bs(Day, knots = NULL)2 | 924.409 **** | |||||
| (114.445) | ||||||
| bs(Day, knots = NULL)3 | -73.495 | |||||
| (98.521) | ||||||
| bs(Day, knots = c(30, 247, 420))1 | -238.760 | |||||
| (189.563) | ||||||
| bs(Day, knots = c(30, 247, 420))2 | 623.211 **** | |||||
| (163.042) | ||||||
| bs(Day, knots = c(30, 247, 420))3 | -176.185 | |||||
| (190.514) | ||||||
| bs(Day, knots = c(30, 247, 420))4 | 1237.844 **** | |||||
| (169.846) | ||||||
| bs(Day, knots = c(30, 247, 420))5 | -925.546 **** | |||||
| (178.335) | ||||||
| bs(Day, knots = c(30, 247, 420))6 | 693.659 **** | |||||
| (178.836) | ||||||
| ar1 | 0.237 | |||||
| (0.106) | ||||||
| ar2 | -0.841 | |||||
| (0.088) | ||||||
| ar3 | -0.127 | |||||
| (0.107) | ||||||
| ar4 | -0.413 | |||||
| (0.047) | ||||||
| ar5 | -0.448 | |||||
| (0.055) | ||||||
| ma1 | -0.945 | |||||
| (0.110) | ||||||
| ma2 | 1.038 | |||||
| (0.162) | ||||||
| ma3 | -0.456 | |||||
| (0.149) | ||||||
| ma4 | 0.366 | |||||
| (0.093) | ||||||
| nobs | 521 | 521 | 521 | 521 | 521 | 520 |
| r.squared | 0.002 | 0.035 | 0.013 | 0.189 | 0.374 | |
| adj.r.squared | -0.000 | 0.033 | 0.011 | 0.185 | 0.367 | |
| sigma | 397.258 | 390.607 | 1.601 | 358.640 | 316.081 | 140.204 |
| statistic | 0.830 | 18.685 | 6.910 | 40.269 | 51.188 | |
| p.value | 0.363 | 0.000 | 0.009 | 0.000 | 0.000 | |
| df | 1.000 | 1.000 | 1.000 | 3.000 | 6.000 | |
| logLik | -3856.235 | -3847.437 | -983.504 | -3801.948 | -3734.618 | -3304.902 |
| AIC | 7718.469 | 7700.875 | 1973.009 | 7613.895 | 7485.236 | 6629.804 |
| BIC | 7731.236 | 7713.642 | 1985.776 | 7635.174 | 7519.282 | 6672.342 |
| deviance | 81905514.761 | 79185735.475 | 1330.515 | 66497947.233 | 51352160.074 | |
| df.residual | 519.000 | 519.000 | 519.000 | 517.000 | 514.000 | |
| nobs.1 | 521.000 | 521.000 | 521.000 | 521.000 | 521.000 | 520.000 |
| **** p < 0.001; *** p < 0.01; ** p < 0.05; * p < 0.1. | ||||||
| Linear | Semilog | Growth | Spline with knots | Spline without knots | Smooth spline | ARIMA | |
|---|---|---|---|---|---|---|---|
| Absolute Error | 150000 | 150000 | 170000 | 120000 | 140000 | 39000 | 42000 |
| Absolute Percent Error | Inf | Inf | Inf | Inf | Inf | Inf | Inf |
| Accuracy | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Adjusted R Square | -0.00033 | 0.033 | 0.011 | 0.37 | 0.18 | 0 | 0 |
| Akaike’s Information Criterion AIC | 7700 | 7700 | 2000 | 7500 | 7600 | 0 | 6600 |
| Allen’s Prediction Sum-Of-Squares (PRESS, P-Square) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Area under the ROC curve (AUC) | 0.0087 | 0.0087 | 0.0087 | 0.14 | 0.04 | 0.0087 | 0.02 |
| Average Precision at k | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Bias | 0.0000000000000089 | -0.000000000000035 | 330 | -0.0000000000000047 | -0.000000000000036 | 0.00000000000011 | 2.5 |
| Brier score | 200000 | 200000 | 300000 | 100000 | 100000 | 20000 | 20000 |
| Classification Error | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| F1 Score | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| fScore | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| GINI Coefficient | 0.05 | 0.05 | 0.05 | 0.8 | 0.6 | 1 | 1 |
| kappa statistic | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Log Loss | Inf | Inf | Inf | Inf | Inf | Inf | Inf |
| Mallow’s cp | 2 | 2 | 2 | 7 | 4 | 0 | 0 |
| Matthews Correlation Coefficient | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Mean Log Loss | Inf | Inf | Inf | Inf | Inf | Inf | Inf |
| Mean Absolute Error | 290 | 280 | 330 | 230 | 260 | 74 | 81 |
| Mean Absolute Percent Error | Inf | Inf | Inf | Inf | Inf | Inf | Inf |
| Mean Average Precision at k | 0 | 0 | 0 | 0 | 0 | 0.2 | 0 |
| Mean Absolute Scaled Error | 3 | 2.9 | 3.4 | 2.3 | 2.7 | 0.76 | 0.84 |
| Median Absolute Error | 250 | 220 | 180 | 190 | 220 | 34 | 42 |
| Mean Squared Error | 160000 | 150000 | 270000 | 99000 | 130000 | 18000 | 19000 |
| Mean Squared Log Error | 3.2 | NaN | 13 | NaN | NaN | 0.28 | 0.28 |
| Model turning point error | 264 | 264 | 264 | 241 | 265 | 248 | 296 |
| Negative Predictive Value | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Percent Bias | -Inf | NaN | -Inf | NaN | NaN | NaN | NaN |
| Positive Predictive Value | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Precision | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| R Square | 0.0016 | 0.035 | 0.013 | 0.37 | 0.19 | 0 | 0 |
| Relative Absolute Error | 1 | 0.98 | 1.2 | 0.79 | 0.9 | 0.26 | 0.28 |
| Recall | 310 | 29 | 4.7 | 9.7 | 10 | -0.18 | 0.45 |
| Root Mean Squared Error | 400 | 390 | 520 | 310 | 360 | 140 | 140 |
| Root Mean Squared Log Error | 1.8 | NaN | 3.6 | NaN | NaN | 0.53 | 0.53 |
| Root Relative Squared Error | 1 | 0.98 | 1.3 | 0.79 | 0.9 | 0.34 | 0.35 |
| Relative Squared Error | 1 | 0.97 | 1.7 | 0.63 | 0.81 | 0.12 | 0.12 |
| Schwarz’s Bayesian criterion BIC | 7700 | 7700 | 2000 | 7500 | 7600 | 0 | 6700 |
| Sensitivity | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| specificity | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Squared Error | 82000000 | 79000000 | 140000000 | 51000000 | 66000000 | 9600000 | 10000000 |
| Squared Log Error | 1700 | NaN | 6700 | NaN | NaN | 150 | 150 |
| Symmetric Mean Absolute Percentage Error | 0.93 | 0.93 | 1.8 | 0.89 | 0.93 | 0.35 | 0.41 |
| Sum of Squared Errors | 82000000 | 79000000 | 140000000 | 51000000 | 66000000 | 9600000 | 10000000 |
| True negative rate | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| True positive rate | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Spline without knots | Spline with knots | ARIMA | Quardratic polynomial | Essembled based on weight | Essembled based on summed weight | |
|---|---|---|---|---|---|---|
| (Intercept) | -4.427 | -5.445 | -73.079 | 63.252 | 5.538 | |
| (62.400) | (56.636) | (47.384) | (58.044) | (12.629) | ||
| bs(Day, knots = NULL)1 | 518.671 *** | |||||
| (180.305) | ||||||
| bs(Day, knots = NULL)2 | 924.409 **** | |||||
| (114.445) | ||||||
| bs(Day, knots = NULL)3 | -73.495 | |||||
| (98.521) | ||||||
| bs(Day, knots = BREAKS)1 | 12.816 | |||||
| (109.491) | ||||||
| bs(Day, knots = BREAKS)2 | 5.594 | |||||
| (70.929) | ||||||
| bs(Day, knots = BREAKS)3 | 856.945 **** | |||||
| (81.316) | ||||||
| bs(Day, knots = BREAKS)4 | 153.515 ** | |||||
| (69.095) | ||||||
| bs(Day, knots = BREAKS)5 | 241.337 *** | |||||
| (75.755) | ||||||
| bs(Day, knots = BREAKS)6 | -145.933 ** | |||||
| (71.460) | ||||||
| bs(Day, knots = BREAKS)7 | 2160.088 **** | |||||
| (71.855) | ||||||
| bs(Day, knots = BREAKS)8 | -515.379 **** | |||||
| (75.125) | ||||||
| bs(Day, knots = BREAKS)9 | 452.093 **** | |||||
| (85.368) | ||||||
| bs(Day, knots = BREAKS)10 | -209.867 ** | |||||
| (81.457) | ||||||
| bs(Day, knots = BREAKS)11 | 583.000 **** | |||||
| (80.978) | ||||||
| ar1 | 0.237 | |||||
| (0.106) | ||||||
| ar2 | -0.841 | |||||
| (0.088) | ||||||
| ar3 | -0.127 | |||||
| (0.107) | ||||||
| ar4 | -0.413 | |||||
| (0.047) | ||||||
| ar5 | -0.448 | |||||
| (0.055) | ||||||
| ma1 | -0.945 | |||||
| (0.110) | ||||||
| ma2 | 1.038 | |||||
| (0.162) | ||||||
| ma3 | -0.456 | |||||
| (0.149) | ||||||
| ma4 | 0.366 | |||||
| (0.093) | ||||||
| Day | 4.497 **** | |||||
| (0.419) | ||||||
| I(Day^2) | -0.008 **** | |||||
| (0.001) | ||||||
| fitf | -2.984 | -0.187 | ||||
| (2.954) | (0.127) | |||||
| fit0f | -1.405 | -0.153 | ||||
| (1.356) | (0.234) | |||||
| fit1f | 2.360 | 0.755 **** | ||||
| (2.923) | (0.146) | |||||
| fitpif | 1.050 | 0.131 | ||||
| (0.945) | (0.235) | |||||
| fitaf | -0.253 | 0.440 **** | ||||
| (1.880) | (0.065) | |||||
| fitf:fit0f | -0.029 | |||||
| (0.021) | ||||||
| fitf:fit1f | 0.002 | |||||
| (0.004) | ||||||
| fit0f:fit1f | 0.040 | |||||
| (0.028) | ||||||
| fitf:fitpif | 0.053 * | |||||
| (0.030) | ||||||
| fit0f:fitpif | 0.001 | |||||
| (0.001) | ||||||
| fit1f:fitpif | -0.051 | |||||
| (0.036) | ||||||
| fitf:fitaf | 0.002 | |||||
| (0.021) | ||||||
| fit0f:fitaf | 0.007 | |||||
| (0.013) | ||||||
| fit1f:fitaf | 0.005 | |||||
| (0.016) | ||||||
| fitpif:fitaf | -0.009 | |||||
| (0.018) | ||||||
| fitf:fit0f:fit1f | -0.000 | |||||
| (0.000) | ||||||
| fitf:fit0f:fitpif | -0.000 | |||||
| (0.000) | ||||||
| fitf:fit1f:fitpif | 0.000 | |||||
| (0.000) | ||||||
| fit0f:fit1f:fitpif | 0.000 | |||||
| (0.000) | ||||||
| fitf:fit0f:fitaf | 0.000 | |||||
| (0.000) | ||||||
| fitf:fit1f:fitaf | -0.000 | |||||
| (0.000) | ||||||
| fit0f:fit1f:fitaf | -0.000 | |||||
| (0.000) | ||||||
| fitf:fitpif:fitaf | -0.000 | |||||
| (0.000) | ||||||
| fit0f:fitpif:fitaf | 0.000 | |||||
| (0.000) | ||||||
| fit1f:fitpif:fitaf | 0.000 | |||||
| (0.000) | ||||||
| fitf:fit0f:fit1f:fitpif | 0.000 | |||||
| (0.000) | ||||||
| fitf:fit0f:fit1f:fitaf | 0.000 | |||||
| (0.000) | ||||||
| fitf:fit0f:fitpif:fitaf | 0.000 | |||||
| (0.000) | ||||||
| fitf:fit1f:fitpif:fitaf | 0.000 | |||||
| (0.000) | ||||||
| fit0f:fit1f:fitpif:fitaf | -0.000 | |||||
| (0.000) | ||||||
| fitf:fit0f:fit1f:fitpif:fitaf | -0.000 | |||||
| (0.000) | ||||||
| nobs | 521 | 521 | 520 | 521 | 521 | 521 |
| r.squared | 0.189 | 0.863 | 0.186 | 0.901 | 0.894 | |
| adj.r.squared | 0.185 | 0.860 | 0.182 | 0.894 | 0.893 | |
| sigma | 358.640 | 148.456 | 140.204 | 359.137 | 129.184 | 130.062 |
| statistic | 40.269 | 292.116 | 59.021 | 142.799 | 866.924 | |
| p.value | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |
| df | 3.000 | 11.000 | 2.000 | 31.000 | 5.000 | |
| logLik | -3801.948 | -3338.349 | -3304.902 | -3803.173 | -3255.458 | -3272.483 |
| AIC | 7613.895 | 6702.698 | 6629.804 | 7614.346 | 6576.916 | 6558.966 |
| BIC | 7635.174 | 6758.022 | 6672.342 | 7631.369 | 6717.355 | 6588.756 |
| deviance | 66497947.233 | 11218017.844 | 66811506.045 | 8160628.858 | 8711782.329 | |
| df.residual | 517.000 | 509.000 | 518.000 | 489.000 | 515.000 | |
| nobs.1 | 521.000 | 521.000 | 520.000 | 521.000 | 521.000 | 521.000 |
| **** p < 0.001; *** p < 0.01; ** p < 0.05; * p < 0.1. | ||||||
| Spline with knots | Spline without knots | Smooth spline | ARIMA | Quardratic polynomial | Essembled equal weight | Essembled on weight | Essembled summed weight | Essembled weight of fit | |
|---|---|---|---|---|---|---|---|---|---|
| Absolute Error | 45000 | 140000 | 39000 | 42000 | 130000 | 180000 | 37000 | 38000 | 180000 |
| Absolute Percent Error | Inf | Inf | Inf | Inf | Inf | Inf | Inf | Inf | Inf |
| Accuracy | 0 | 0 | 0 | 0 | 0 | 0.035 | 0 | 0 | 0.035 |
| Adjusted R Square | 0.86 | 0.18 | 0 | 0 | 0.18 | 0 | 0.89 | 0.89 | 0 |
| Akaike’s Information Criterion AIC | 6700 | 7600 | 0 | 6600 | 7600 | 0 | 6600 | 6600 | 0 |
| Allen’s Prediction Sum-Of-Squares (PRESS, P-Square) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Area under the ROC curve (AUC) | 0.0087 | 0.04 | 0.0087 | 0.02 | 0.0087 | 0.0087 | 0.076 | 0.0096 | 0.0087 |
| Average Precision at k | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0.5 |
| Bias | 0.0000000000000012 | -0.000000000000036 | 0.00000000000011 | 2.5 | 0.000000000000042 | 340 | -0.00000000000000054 | -0.0000000000000015 | 340 |
| Brier score | 20000 | 100000 | 20000 | 20000 | 100000 | 300000 | 20000 | 20000 | NaN |
| Classification Error | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| F1 Score | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| fScore | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| GINI Coefficient | 1 | 0.6 | 1 | 1 | 0.5 | 0.9 | 1 | 1 | 0.9 |
| kappa statistic | 0 | 0 | 0 | 0 | 0 | NaN | 0 | 0 | NaN |
| Log Loss | Inf | Inf | Inf | Inf | Inf | Inf | Inf | Inf | Inf |
| Mallow’s cp | 12 | 4 | 0 | 0 | 3 | 0 | 0 | 6 | 0 |
| Matthews Correlation Coefficient | 0 | 0 | 0 | 0 | 0 | NaN | 0 | 0 | NaN |
| Mean Log Loss | Inf | Inf | Inf | Inf | Inf | NaN | Inf | Inf | NaN |
| Mean Absolute Error | 87 | 260 | 74 | 81 | 260 | 340 | 70 | 72 | NaN |
| Mean Absolute Percent Error | Inf | Inf | Inf | Inf | Inf | Inf | Inf | Inf | Inf |
| Mean Average Precision at k | 0 | 0 | 0.2 | 0 | 0 | 0 | 0 | 0 | 0 |
| Mean Absolute Scaled Error | 0.89 | 2.7 | 0.76 | 0.84 | 2.6 | 3.5 | 0.72 | 0.74 | 3.5 |
| Median Absolute Error | 51 | 220 | 34 | 42 | 210 | 98 | 37 | 35 | 130 |
| Mean Squared Error | NA | NA | NA | NA | NA | 270000 | NA | NA | NaN |
| Mean Squared Log Error | NaN | NaN | 0.28 | 0.28 | NaN | 28 | NaN | NaN | 28 |
| Model turning point error | 253 | 265 | 248 | 296 | 264 | 281 | 234 | 282 | 275 |
| Negative Predictive Value | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Percent Bias | NaN | NaN | NaN | NaN | NaN | NaN | -Inf | NaN | NaN |
| Positive Predictive Value | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Precision | NaN | NaN | NaN | NaN | NaN | 0 | NaN | NaN | 0 |
| R Square | 0.86 | 0.19 | 0 | 0 | 0.19 | 0 | 0.9 | 0.89 | 0 |
| Relative Absolute Error | 0.3 | 0.9 | 0.26 | 0.28 | 0.89 | 0.44 | 0.24 | 0.25 | 0.6 |
| Recall | -2.9 | 10 | -0.18 | 0.45 | -47 | 0 | 17 | -1.6 | 0 |
| Root Mean Squared Error | NA | NA | NA | NA | NA | 520 | NA | NA | NaN |
| Root Mean Squared Log Error | NaN | NaN | 0.53 | 0.53 | NaN | 5.3 | NaN | NaN | 5.3 |
| Root Relative Squared Error | 0.37 | 0.9 | 0.34 | 0.35 | 0.9 | 1.3 | 0.32 | 0.33 | 1.3 |
| Relative Squared Error | 0.14 | 0.81 | 0.12 | 0.12 | 0.81 | 1.7 | 0.099 | 0.11 | 1.7 |
| Schwarz’s Bayesian criterion BIC | 6800 | 7600 | 0 | 6700 | 7600 | 0 | 6700 | 6600 | 0 |
| Sensitivity | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0.5 |
| specificity | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Squared Error | 11000000 | 66000000 | 9600000 | 10000000 | 67000000 | 140000000 | 8200000 | 8700000 | 140000000 |
| Squared Log Error | NaN | NaN | 150 | 150 | NaN | 14000 | NaN | NaN | 14000 |
| Symmetric Mean Absolute Percentage Error | 0.49 | 0.93 | 0.35 | 0.41 | 0.89 | 0.59 | 0.41 | 0.36 | 0.71 |
| Sum of Squared Errors | 11000000 | 66000000 | 9600000 | 10000000 | 67000000 | 140000000 | 8200000 | 8700000 | 140000000 |
| True negative rate | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| True positive rate | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Linear | Semilog | Growth | |
|---|---|---|---|
| (Intercept) | 309.718 **** | -61.807 | 4.679 **** |
| (34.859) | (93.889) | (0.140) | |
| Day | 0.105 | 0.001 *** | |
| (0.116) | (0.000) | ||
| log(Day) | 75.814 **** | ||
| (17.539) | |||
| nobs | 521 | 521 | 521 |
| r.squared | 0.002 | 0.035 | 0.013 |
| adj.r.squared | -0.000 | 0.033 | 0.011 |
| sigma | 397.258 | 390.607 | 1.601 |
| statistic | 0.830 | 18.685 | 6.910 |
| p.value | 0.363 | 0.000 | 0.009 |
| df | 1.000 | 1.000 | 1.000 |
| logLik | -3856.235 | -3847.437 | -983.504 |
| AIC | 7718.469 | 7700.875 | 1973.009 |
| BIC | 7731.236 | 7713.642 | 1985.776 |
| deviance | 81905514.761 | 79185735.475 | 1330.515 |
| df.residual | 519.000 | 519.000 | 519.000 |
| nobs.1 | 521.000 | 521.000 | 521.000 |
| **** p < 0.001; *** p < 0.01; ** p < 0.05; * p < 0.1. | |||